In a concrete structure, damage such as a cavity occurs inside a concrete structure owing to wind, rain and temperature variation over many years. Such a structure, for detecting abnormality with the structure such as a cavity, is equipped with means for detecting an abnormal sound with regard to a sound or an oscillation generated by hitting a concrete structure using a hammer, and for monitoring whether there is abnormality with the structure based on the detected value of the abnormal sound.                As a technology of detecting a similarity between a standard sound and an input sound as a geometric distance, the gazette of Japanese Patent No. 3426905 (Japanese Patent Application No. Hei 9(1997)-61007, Title of the Invention: Method for detecting an abnormal sound and method for judging abnormality in machine by use of detected value thereof, and method for detecting similarity between oscillation waves and method for recognizing voice by use of detected value thereof) is known.        As an improved technology of detecting a similarity between standard information and input information as a geometric distance, the gazette of Japanese Patent No. 3342864 (Japanese Patent Application No. 2000-277749, Title of the Invention: Method for detecting similarity between voices and method for recognizing voice by use of detected value thereof, method for detecting similarity between oscillation waves and method for judging abnormality in machine by use of detected value thereof, method for detecting similarity between images and method for recognizing image by use of detected value thereof, method for detecting similarity between solids and method for recognizing solid by use of detected value thereof, and method for detecting similarity between moving images and method for recognizing moving image by use of detected value thereof) is known.        As a further improved technology of detecting a similarity between standard information and input information as a geometric distance, the gazette of Japanese Patent No. 3422787 (Japanese Patent Application No. 2002-68231, Title of the Invention: Method for detecting similarity between images and method for recognizing image by use of detected value thereof, method for detecting similarity between voices and method for recognizing voice by use of detected value thereof, method for detecting similarity between oscillation waves and method for judging abnormality in machine by use of detected value thereof, method for detecting similarity between moving images and method for recognizing moving image by use of detected value thereof, and method for detecting similarity between solids and method for recognizing solid by use of detected value thereof) is known.        
The method for detecting a similarity between standard information and input information in the above three prior arts includes the steps of: registering in advance a standard pattern vector having, as a component, a feature quantity such as a power spectrum of a standard sound; creating an input pattern vector having a feature quantity of an input sound as a component; and calculating the degree of similarity between the standard pattern vector and the input pattern vector as a geometric distance. Moreover, the method for detecting an abnormal sound in the above three prior arts includes the step of: comparing a calculated value of the geometric distance with an arbitrarily set allowed value.
Incidentally, in statistical analysis, a normal distribution is usually used as a model of a phenomenon. Then, a “kurtosis” and a “skewness” are used to verify whether the phenomenon obeys the normal distribution or not. Here, the kurtosis and the skewness are statistics. If a probability distribution of the phenomenon follows the normal distribution, then a value of the kurtosis is equal to 3. If it has peakedness relative to the normal distribution, then a value of the kurtosis is greater than 3. Conversely, if it has flatness relative to the normal distribution, then a value of the kurtosis is less than 3. Also, if a probability distribution of the phenomenon is symmetrical about the center axis, then a value of the skewness is equal to 0. If the tail on the right side of the probability distribution is longer than the left side, then a value of the skewness is greater than 0. Conversely, if the tail on the left side of the probability distribution is longer than the right side, then a value of the skewness is less than 0.
In the prior arts, the degree of similarity between the standard pattern vector and the input pattern vector is calculated as a geometric distance by using only a “kurtosis”. In the present invention, the degree of similarity between the standard pattern vector and the input pattern vector is calculated as a new geometric distance by using both “kurtosis” and “skewness”. Therefore, in order to distinguish “kurtosis” from “skewness” and describe them clearly, we change names from a “weighting vector” and a “weighting curve” in the prior art (the gazette of Japanese Patent No. 3422787) into a “kurtosis-weighting vector” and a “kurtosis-weighting curve” in the present invention, respectively. Also, we change names from an “original and weighted standard pattern vector” and an “original and weighted input pattern vector” in the prior art (the gazette of Japanese Patent No. 3422787) into a “kurtosis-weighted standard pattern vector” and a “kurtosis-weighted input pattern vector” in the present invention, respectively. Further, we change a name from a “geometric distance” in the prior arts (the gazette of Japanese Patent No. 3426905, No. 3342864 and No. 3422787) into a “kurtosis geometric distance” in the present invention.
In the method of calculating the kurtosis geometric distance of the prior arts, a difference in shapes between standard and input patterns is replaced by a shape change in a reference shape (a reference pattern) such as a normal distribution, and the magnitude of this shape change is numerically evaluated as a variable of the kurtosis. Then, the variable of the kurtosis is calculated while moving the center axis of the reference pattern to a position of each component of the standard and input patterns, and the kurtosis geometric distance is calculated by using these variables of the kurtosis. Note that, in the prior art (the gazette of Japanese Patent No. 3422787), the approximate value of the variable of the kurtosis is calculated, instead of calculating the variable of the kurtosis directly.
In general, an equation for calculating the kurtosis of a vector cannot be defined if the component value of the vector is negative. Therefore, in the prior arts, positive and negative reference pattern vectors that have a normal distribution as their initial shapes are created, and a difference in shapes between standard and input patterns is replaced by the shape changes of the positive and negative reference pattern vectors so that the component value of the vector may not become negative. However, in the case where the difference in shapes between standard and input patterns is small, the component value of the vector does not become negative even if we use a method where the difference in shapes between standard and input patterns is replaced by the shape change in a single reference pattern vector. If we explain a principle of the prior arts by using the latter method instead of the former method, it is easier to understand. Therefore, in the following, we explain the principle of the prior arts by using a single reference pattern vector (a single shape of reference pattern). Namely, we explain the prior arts by using the method where the component value of a single reference pattern changes by a difference obtained by subtracting the component value of the standard pattern from the component value of the input pattern, and the magnitude of this shape change is numerically evaluated as a variable of the kurtosis.
The upper and middle diagrams of FIGS. 53(a) to 53(e) show a typical example of the shapes of the standard and input pattern vectors, respectively. FIGS. 53(a) to 53(d) each show the standard and input patterns having a single peak. FIG. 53(e) typically shows the standard pattern having a flat shape and the input pattern where a “wobble” occurs in the flat shape. Also, the bottom diagrams of FIGS. 53(a) to 53(e) show an example where a difference in shapes between the standard and input patterns is replaced by the shape change in the reference pattern having the normal distribution as its initial shape. Note that the peaks of the standard and input patterns shown in FIGS. 53(a) to 53(d) are assumed to have the same height, and the area of each standard pattern and each input pattern shown in FIGS. 53(a) to 53(e) is equal to 1.                FIG. 53(a) gives an example of the case where standard pattern and input pattern have the same shape. Since the reference pattern does not change in its shape from the normal distribution during this time, the kurtosis becomes A=3.        FIGS. 53(b), 53(c) and 53(d) each show an example exhibiting a small, medium, and large “difference” of peaks between the standard and input patterns. During this time, the component value of the reference pattern decreases by the absolute value of the difference between the component value of the standard pattern and the component value of the input pattern at peak position of each standard pattern. At the same time, the component value of the reference pattern increases by the absolute value of the difference between the component value of the standard pattern and the component value of the input pattern at peak position of each input pattern.        In FIG. 53(b), the position of the decreased component value of the reference pattern and that of the increased component value of the reference pattern are close. Since the effect of a decrease and an increase is cancelled out, the kurtosis becomes A≈3.        In FIG. 53(d), since the shape of the reference pattern has flatness relative to the normal distribution, the kurtosis becomes A<<3.        In FIG. 53(c), since the shape of the reference pattern is an intermediate state between FIG. 53(b) and FIG. 53(d), the kurtosis becomes A<3.        
Therefore, from FIGS. 53(a) to 53(d), we can understand that the value of the kurtosis decreases monotonically as the “difference” increases between peaks of the standard and input patterns.                In FIG. 53(e), the reference pattern has a small shape change from the normal distribution, because the shape of the reference pattern increases and decreases alternately by the absolute value of the difference between the component value of the standard pattern and the component value of the input pattern. The kurtosis becomes A≈3. Also, if the shape of the reference pattern increases and decreases randomly, the kurtosis becomes A≈3.        
In the method for calculating the kurtosis geometric distance of the prior arts, the variable of the kurtosis is obtained by subtracting 3 from the value of the kurtosis. Then, the variable of the kurtosis is calculated while moving the center axis of the reference pattern to a position of each component of the standard and input patterns, and the kurtosis geometric distance is obtained by calculating a square root of a sum of each variable of kurtosis squared. Thus, when a “difference” occurs between peaks of the standard and input patterns with “wobble” due to noise or the like, the “wobble” is absorbed and the kurtosis geometric distance increases monotonically as the “difference” increases.